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Al-Mazrooei, A. E.; Latif, A.; Yao, J. C.

Solving generalized mixed equilibria, variational inequalities, and constrained convex minimization. (English) Zbl 1473.47027

Abstr. Appl. Anal. 2014, Article ID 587865, 26 p. (2014).
Summary: We propose implicit and explicit iterative algorithms for finding a common element of the set of solutions of the minimization problem for a convex and continuously Fréchet differentiable functional, the set of solutions of a finite family of generalized mixed equilibrium problems, and the set of solutions of a finite family of variational inequalities for inverse strong monotone mappings in a real Hilbert space. We prove that the sequences generated by the proposed algorithms converge strongly to a common element of three sets, which is the unique solution of a variational inequality defined over the intersection of three sets under very mild conditions.

Cited in 5 Documents

MSC:

47J25 Iterative procedures involving nonlinear operators
49J40 Variational inequalities

Keywords:

implicit iterative algorithms; minimization problem; real Hilbert space; strong convergence
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\textit{A. E. Al-Mazrooei} et al., Abstr. Appl. Anal. 2014, Article ID 587865, 26 p. (2014; Zbl 1473.47027)
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